The aggregation method preserves the order of accuracy if the aggregate size is proportional to the background mesh size. The ratio between the aggregate size and root element size is related to the geometry of the domain boundary (see [1]} for more details) and can be improved with refinement (for a given definition of the domain boundary \(\partial \Omega \) ). For a fixed mesh representation of the domain boundary (the standard situation), the assumption that the aggregate size is proportional to the background mesh size holds for \(h\)  small enough.
